Question

Find the inverse of the function
`g(x) = (4)/( - x - 3 ) - 2`

Answer 1

Given:

The function is,

`\begin{gathered} g(x)=(4)/(-x-3)-2 \\ y=(4)/(-x-3)-2 \end{gathered}`

The objective is to find the inverse of the function.

To find the inverse of a function, interchange the variables x and y and solve for y.

Then, the above equation can be represented as,

`\begin{gathered} x=(4)/(-y-3)-2 \\ x+2=(4)/(-y-3) \\ -y-3=(4)/(x+2) \end{gathered}`